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Math Help - finding the rate of change of height of cone.

  1. #1
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    finding the rate of change of height of cone.

    maths prob.bmp

    Hi guys, i am having problem to solve the above question, i seem not able to get the correct answer each time i try out.

    Hope someone could help me out. Thanks.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: finding the rate of change of height of cone.

    Think of the volume V of water in the conical container as being composed of circular disks of thickness dh. We may then state:

    \frac{dV}{dt}=\pi r^2\frac{dh}{dt}

    We know the ratio of the radius of the water's surface to the height of the water level will be the same as that of the container:

    r=\frac{2}{3}h hence:

    \frac{dV}{dt}=\pi \left(\frac{2}{3}h \right)^2\frac{dh}{dt}

    Now, solve for \frac{dh}{dt} and use the given values of \frac{dV}{dt},h to compute the requested value.
    Thanks from vetri
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